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paper/paper.bib

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@article{brunet_multidimensional_2024,
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title = {Multidimensional {Analysis} of the {Adult} {Human} {Heart} in {Health} and {Disease} {Using} {Hierarchical} {Phase}-{Contrast} {Tomography}},
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volume = {312},
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issn = {0033-8419, 1527-1315},
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url = {http://pubs.rsna.org/doi/10.1148/radiol.232731},
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doi = {10.1148/radiol.232731},
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abstract = {Hierarchical phase-contrast tomography (HiP-CT) enables ex vivo virtual autopsy cardiac imaging with high spatial resolution, providing nondestructive, three-dimensional, multiscale analysis of intact healthy and diseased adult human hearts without contrast agents.
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Background Current clinical imaging modalities such as CT and MRI provide resolution adequate to diagnose cardiovascular diseases but cannot depict detailed structural features in the heart across length scales. Hierarchical phase-contrast tomography (HiP-CT) uses fourth-generation synchrotron sources with improved x-ray brilliance and high energies to provide micron-resolution imaging of intact adult organs with unprecedented detail. Purpose To evaluate the capability of HiP-CT to depict the macro- to microanatomy of structurally normal and abnormal adult human hearts ex vivo. Materials and Methods Between February 2021 and September 2023, two adult human donor hearts were obtained, fixed in formalin, and prepared using a mixture of crushed agar in a 70\% ethanol solution. One heart was from a 63-year-old White male without known cardiac disease, and the other was from an 87-year-old White female with a history of multiple known cardiovascular pathologies including ischemic heart disease, hypertension, and atrial fibrillation. Nondestructive ex vivo imaging of these hearts without exogenous contrast agent was performed using HiP-CT at the European Synchrotron Radiation Facility. Results HiP-CT demonstrated the capacity for high-spatial-resolution, multiscale cardiac imaging ex vivo, revealing histologic-level detail of the myocardium, valves, coronary arteries, and cardiac conduction system across length scales. Virtual sectioning of the cardiac conduction system provided information on fatty infiltration, vascular supply, and pathways between the cardiac nodes and adjacent structures. HiP-CT achieved resolutions ranging from gross (isotropic voxels of approximately 20 µm) to microscopic (approximately 6.4-µm voxel size) to cellular (approximately 2.3-µm voxel size) in scale. The potential for quantitative assessment of features in health and disease was demonstrated. Conclusion HiP-CT provided high-spatial-resolution, three-dimensional images of structurally normal and diseased ex vivo adult human hearts. Whole-heart image volumes were obtained with isotropic voxels of approximately 20 µm, and local regions of interest were obtained with resolution down to 2.3–6.4 µm without the need for sectioning, destructive techniques, or exogenous contrast agents. Published under a CC BY 4.0 license Supplemental material is available for this article. See also the editorial by Bluemke and Pourmorteza in this issue.},
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language = {en},
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number = {1},
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urldate = {2025-06-19},
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journal = {Radiology},
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author = {Brunet, Joseph and Cook, Andrew C. and Walsh, Claire L. and Cranley, James and Tafforeau, Paul and Engel, Klaus and Arthurs, Owen and Berruyer, Camille and Burke O’Leary, Emer and Bellier, Alexandre and Torii, Ryo and Werlein, Christopher and Jonigk, Danny D. and Ackermann, Maximilian and Dollman, Kathleen and Lee, Peter D.},
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month = jul,
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year = {2024},
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pages = {e232731},
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}
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@article{teh_validation_2016,
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title = {Validation of diffusion tensor {MRI} measurements of cardiac microstructure with structure tensor synchrotron radiation imaging},
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volume = {19},
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issn = {10976647},
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url = {https://linkinghub.elsevier.com/retrieve/pii/S1097664723010657},
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doi = {10.1186/s12968-017-0342-x},
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language = {en},
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number = {1},
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urldate = {2025-07-28},
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journal = {Journal of Cardiovascular Magnetic Resonance},
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author = {Teh, Irvin and McClymont, Darryl and Zdora, Marie-Christine and Whittington, Hannah J. and Davidoiu, Valentina and Lee, Jack and Lygate, Craig A. and Rau, Christoph and Zanette, Irene and Schneider, Jürgen E.},
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month = dec,
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year = {2016},
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pages = {31},
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file = {Full Text:C\:\\Users\\joseph08091994\\Zotero\\storage\\KGALIM56\\Teh et al. - 2016 - Validation of diffusion tensor MRI measurements of cardiac microstructure with structure tensor sync.pdf:application/pdf},
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}
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@article{tournier_mrtrix3_2019,
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title = {{MRtrix3}: {A} fast, flexible and open software framework for medical image processing and visualisation},
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volume = {202},
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issn = {10538119},
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shorttitle = {{MRtrix3}},
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url = {https://linkinghub.elsevier.com/retrieve/pii/S1053811919307281},
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doi = {10.1016/j.neuroimage.2019.116137},
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language = {en},
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urldate = {2025-07-28},
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journal = {NeuroImage},
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author = {Tournier, J-Donald and Smith, Robert and Raffelt, David and Tabbara, Rami and Dhollander, Thijs and Pietsch, Maximilian and Christiaens, Daan and Jeurissen, Ben and Yeh, Chun-Hung and Connelly, Alan},
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month = nov,
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year = {2019},
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pages = {116137},
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file = {Full Text:C\:\\Users\\joseph08091994\\Zotero\\storage\\BJY4IHV6\\Tournier et al. - 2019 - MRtrix3 A fast, flexible and open software framework for medical image processing and visualisation.pdf:application/pdf},
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}
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@article{garyfallidis_dipy_2014,
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title = {Dipy, a library for the analysis of diffusion {MRI} data},
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volume = {8},
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issn = {1662-5196},
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url = {http://journal.frontiersin.org/article/10.3389/fninf.2014.00008/abstract},
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doi = {10.3389/fninf.2014.00008},
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urldate = {2025-07-28},
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journal = {Frontiers in Neuroinformatics},
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author = {Garyfallidis, Eleftherios and Brett, Matthew and Amirbekian, Bagrat and Rokem, Ariel and Van Der Walt, Stefan and Descoteaux, Maxime and Nimmo-Smith, Ian and {Dipy Contributors}},
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month = feb,
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year = {2014},
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file = {Full Text:C\:\\Users\\joseph08091994\\Zotero\\storage\\YS4L96GS\\Garyfallidis et al. - 2014 - Dipy, a library for the analysis of diffusion MRI data.pdf:application/pdf},
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}
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@article{yeh_dsi_2025,
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title = {{DSI} {Studio}: an integrated tractography platform and fiber data hub for accelerating brain research},
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issn = {1548-7091, 1548-7105},
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shorttitle = {{DSI} {Studio}},
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url = {https://www.nature.com/articles/s41592-025-02762-8},
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doi = {10.1038/s41592-025-02762-8},
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language = {en},
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urldate = {2025-07-28},
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journal = {Nature Methods},
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author = {Yeh, Fang-Cheng},
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month = jul,
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year = {2025},
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}
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@article{mekkaoui_diffusion_2017,
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title = {Diffusion {MRI} in the heart},
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volume = {30},
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copyright = {http://creativecommons.org/licenses/by-nc-nd/4.0/},
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issn = {0952-3480, 1099-1492},
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url = {https://analyticalsciencejournals.onlinelibrary.wiley.com/doi/10.1002/nbm.3426},
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doi = {10.1002/nbm.3426},
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abstract = {Diffusion MRI provides unique information on the structure, organization, and integrity of the myocardium without the need for exogenous contrast agents. Diffusion MRI in the heart, however, has proven technically challenging because of the intrinsic non‐rigid deformation during the cardiac cycle, displacement of the myocardium due to respiratory motion, signal inhomogeneity within the thorax, and short transverse relaxation times. Recently developed accelerated diffusion‐weighted MR acquisition sequences combined with advanced post‐processing techniques have improved the accuracy and efficiency of diffusion MRI in the myocardium. In this review, we describe the solutions and approaches that have been developed to enable diffusion MRI of the heart
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in vivo
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, including a dual‐gated stimulated echo approach, a velocity‐ (
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M
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) or an acceleration‐ (
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M
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) compensated pulsed gradient spin echo approach, and the use of principal component analysis filtering. The structure of the myocardium and the application of these techniques in ischemic heart disease are also briefly reviewed. The advent of clinical MR systems with stronger gradients will likely facilitate the translation of cardiac diffusion MRI into clinical use. The addition of diffusion MRI to the well‐established set of cardiovascular imaging techniques should lead to new and complementary approaches for the diagnosis and evaluation of patients with heart disease. © 2015 The Authors.
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NMR in Biomedicine
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published by John Wiley \& Sons Ltd.},
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language = {en},
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number = {3},
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urldate = {2025-07-28},
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journal = {NMR in Biomedicine},
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author = {Mekkaoui, Choukri and Reese, Timothy G. and Jackowski, Marcel P. and Bhat, Himanshu and Sosnovik, David E.},
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month = mar,
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year = {2017},
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pages = {e3426},
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file = {Full Text:C\:\\Users\\joseph08091994\\Zotero\\storage\\39X9SFK8\\Mekkaoui et al. - 2017 - Diffusion MRI in the heart.pdf:application/pdf},
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}

paper/paper.md

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title: 'Cardiotensor: A Python Library for Orientation Analysis and Tractography in 3D Cardiac Imaging'
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tags:
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- Python
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- cardiac imaging
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- structure tensor
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- orientation analysis
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- histoanatomy
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- fiber architecture
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- heart
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authors:
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- name: Joseph Brunet
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orcid:
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affiliation: "1, 2"
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- name: Lisa Chestnutt
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orcid:
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affiliation: 3
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- name: Andrew Cook
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orcid:
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affiliation: 3
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- name: Hector Dejea
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orcid:
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affiliation: 2
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- name: Matthieu Chourrout
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orcid:
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affiliation: 1
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- name: David Stansby
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orcid:
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affiliation: 1
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- name: Peter D. Lee
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orcid:
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affiliation: "1, 4"
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affiliations:
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- name: Department of Mechanical Engineering, University College London, London, UK
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index: 1
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- name: European Synchrotron Radiation Facility, Grenoble, France
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index: 2
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- name: UCL Institute of Cardiovascular Science, London, UK
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index: 3
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- name: Research Complex at Harwell, Didcot, UK
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index: 4
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date: 26 June 2025
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bibliography: paper.bib
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---
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# Summary
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Understanding the architecture of the human heart requires analyzing its microstructural organization across scales. With the advent of high-resolution imaging techniques such as synchrotron-based tomography, it has become possible to visualize entire hearts at micron-scale resolution. However, translating these large, complex volumetric datasets into interpretable, quantitative descriptors of cardiac organization remains a major bottleneck.
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Cardiotensor is an open-source Python package designed to quantify 3D cardiomyocyte orientation in whole-heart imaging datasets. It provides efficient, scalable implementations of structure tensor analysis, enabling extraction of directional metrics such as helix angle (HA), transverse angle (TA), and fractional anisotropy (FA). The package supports datasets reaching teravoxel scale and is optimized for high-performance computing environments, including parallel and chunk-based processing pipelines. In addition, cardiotensor includes tractography functionality to reconstruct continuous cardiomyocyte trajectories. This enables fiber-level visualization and structural mapping of cardiac tissue, supporting detailed assessments of anatomical continuity and regional organization.
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By enabling scalable and reproducible analysis of cardiac microstructure, cardiotensor helps researchers study heart development, disease, and anatomy in 3D.
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# Statement of Need
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Despite major advances in high-resolution 3D imaging, there is a lack of scalable, open-source tools to analyze cardiomyocyte orientation in large volumetric datasets. Most established frameworks were developed for diffusion tensor MRI (DT-MRI), where orientation is inferred from water diffusion. Examples include MRtrix3 [@tournier_mrtrix3_2019], DIPY [@garyfallidis_dipy_2014], and DSI Studio [@yeh_dsi_2010]. While powerful for diffusion-based neuroimaging and cardiac applications [@mekkaoui_diffusion_2017], these packages are not designed to handle direct image-gradient–based orientation estimation or the teravoxel-scale datasets produced by synchrotron tomography, micro-CT, or optical imaging.
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For non-diffusion imaging modalities, researchers have historically relied on custom structure tensor implementations to estimate fiber orientation directly from image intensity gradients. However, most of these are in-house codes, often unpublished or not generalizable. For example, structure tensor analysis has been applied in the heart using micro-CT [@], optical projection tomography [@], confocal microscopy [@dileep2023], episcopic microscopy [@], and synchrotron tomography [@], but these methods were tailored to specific datasets and lacked scalability or public availability.
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These datasets present unique computational and analytical challenges, including memory constraints, limited processing throughput, and the need for spatially coherent orientation quantification across large fields of view. Moreover, the diversity of contrast mechanisms in non-diffusion imaging modalities requires algorithms that do not rely on water diffusion but instead exploit local image gradient patterns.
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`cardiotensor` addresses this methodological gap by offering an open-source Python package specifically tailored to structure tensor analysis of high-resolution cardiac volumes. Rather than relying on diffusion modeling, `cardiotensor` infers tissue orientation directly from image intensity gradients, making it applicable across a wide range of modalities. Previous studies have demonstrated strong agreement between structure tensor–based orientation and DT-MRI–derived metrics when applied to the same human hearts [@teh_validation_2016].
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The package supports full pipelines from raw image stacks to fiber orientation maps, HA and TA computation, FA, and tractography. Its architecture is optimized for large datasets, using chunked and parallel processing suitable for high-performance computing environments.
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`cardiotensor` has already been successfully applied in published work to characterize 3D cardiomyocyte architecture in healthy and diseased human hearts using synchrotron tomography [@brunet_multidimensional_2024] to datasets over a terabyte in size, demonstrating its robustness and scalability.
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<img src="https://github.com/JosephBrunet/cardiotensor/raw/main/paper/figs/pipeline.jpg" alt="Helix angle map computed from a human heart dataset using `cardiotensor`." style="max-width: 80%">
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**Figure 1**: Helix angle map computed from a human heart dataset using `cardiotensor`.
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Image Stack + rendeirng -> vector field -> HA/IA/FA + Fiber tracing
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The package also supports centerline interpolation and alignment to anatomical axes, which is useful for regional analysis of the heart.
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# Architecture
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The core functionality of `cardiotensor` is organized into four main modules:
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- **`orientation/`**: Implements the structure tensor framework for estimating local cardiomyocyte orientation. This includes structure-tensor computation, eigenvalue decomposition, rotation to cylindrical coordinate system, and quantification of helix and transverse angles, as well as fractional anisotropy (FA).
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- **`tractography/`**: Provides tools for generating and filtering streamlines that trace cardiomyocyte trajectories based on the orientation field. This module enables fiber-level reconstruction and visualization.
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- **`analysis/`**: Contains higher-level methods that integrate orientation and tractography data for regional or statistical analysis. It also supports interpolation, centerline alignment, and cardiac anatomical mapping.
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- **`utils/`**: Includes general-purpose utilities such as I/O functions, image preprocessing, vector math, and configuration parsing. These functions support the broader package infrastructure.
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This modular structure promotes clarity, reproducibility, and ease of extension for cardiac imaging researchers working with large 3D datasets.
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## Online Documentation
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The documentation for cardiotensor is available online at:
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**[https://josephbrunet.github.io/cardiotensor](https://josephbrunet.github.io/cardiotensor)**
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The main components of the documentation are:
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* Step-by-step walkthroughs for installation, first steps, and a guided example covering all available commands. A small example dataset and its corresponding mask are provided with the package.
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* In-depth explanations of the core algorithms used in cardiotensor, including structure tensor theory, helix angle calculation, fractional anisotropy (FA), and tractography integration.
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* Reference guides for the command-line interface, configuration file format, and public API.
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# Acknowledgements
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This project has been made possible in part by grant number 2022-316777 from the Chan Zuckerberg Initiative DAF, an advised fund of Silicon Valley Community Foundation.
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The authors also acknowledge ESRF beamtimes md1252, md1290, and md1389 as sources of the data.
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AC’s research is enabled through the Noé Heart Centre Laboratories, which are gratefully supported by the Rachel Charitable Trust via Great Ormond Street Hospital Children’s Charity (GOSH Charity). The Noé Heart Centre Laboratories are based in The Zayed Centre for Research into Rare Disease in Children, which was made possible thanks to Her Highness Sheikha Fatima bint Mubarak, wife of the late Sheikh Zayed bin Sultan Al Nahyan, founding father of the United Arab Emirates, as well as other generous funders.
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# References
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